Conformal dimension of the antenna set

被引：15

作者：

Bishop, CJ ^{[1
]}

Tyson, JT ^{[1
]}

机构：

[1] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 12期

关键词：

Quasiconformal map; Hausdorff dimension; conformal dimension; self-similar sets;

D O I：

10.1090/S0002-9939-01-05982-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the self-similar set known as the "antenna set" has the property that inf(f) dim(f(X)) = 1 (where the infimum is over all quasiconformal mappings of the plane), but that this infimum is not attained by any quasiconformal map; indeed, is not attained for any quasisymmetric map into any metric space.

引用

页码：3631 / 3636

页数：6

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